1. Field of the Invention
The present invention relates to a linear differential amplifier which constitutes a part of an electric filter or a similar device to be incorporated, for example, in an IC.
2. Description of the Prior Art
Recently, it has become a common practice to incorporate electric filters comprised of differential amplifiers in an IC. But, a differential amplifier of the operational amplifier type with double amplification stages does not possess a satisfactory frequency characteristic in the high-frequency range such as the video frequency range. Because of this, an electric filter is often realized by constructing a gyrator or a biquad filter with a differential amplifier including a capacitor as a load, which is regarded as a single stage integrator. Such a differential amplifier is shown in FIG. 1, where it is comprised of a pair of bipolar transistors 141 and 142 which form an emitter-coupled pair 143, a capacitor 144 connected between collectors of the transistors 141 and 142 as a load, a constant current source 145 connected between the ground and emitters of the transistors 141 and 142 as a load, a constant current source 145 connected between the ground and emitters of the transistors 141 and 142 for supplying emitter currents 2I.sub.e, load resistors or their equivalents 146 and 147 connected to the collectors of the transistors 141 and 142, output terminals 148A and 148B connected to the collectors of the transistors 141 and 142, and input terminals 149A and 149B connected to bases of the transistors 141 and 142. In FIG. 1, V.sub.cc stands for the power source voltage.
However, an emitter-coupled pair formed by bipolar transistors like the one shown in FIG. 1 possesses poor linearity and changes its transconductance depending on the level of input signals. Consequently, an electric filter comprised of a differential amplifier of this type changes its characteristic depending on the level of input signals, and therefore is not satisfactory in this respect.
There has been proposed a differential amplifier with an improved linearity, such as the one shown in FIG. 2, which has been disclosed by J. O. Voorman et al. in "Bipolar integration of analog gyrator and Laguerre type filters" Proc. ECCTD '83, Stuttgart, pp. 108-110. This differential amplifier is comprised of two emitter-coupled pairs 140 and 150 formed by a pair of transistors 151 and 152, and 153 and 154, respectively, where each of the transistors 152 and 153 has an emitter area four times larger than that of the transistors 151 and 153. Collectors of the transistors 152 and 153 are connected with each other as well as with a load resistor 146 which converts output current I.sub.3 of these two transistors, while collectors of transistors 151 and 154 are connected with each other as well as with a load resistor 147 which converts output currents I.sub.4 of these two transistors. It further includes a constant current source 155 for the emitter-coupled pair 140 for supplying emitter current I.sub.e, and a constant current source 156 for the emitter-coupled pair 150 for supplying emitter currents I.sub.e, output terminals 148A and 149B connected to the collectors of the transistors 152 and 153, and 151 and 154, respectively, input terminals 149A and 149B connected to the bases of the transistors 152 and 153, and 151 and 154, respectively. As in FIG. 1, Vcc stands for the power source voltage in FIG. 2.
The improvement in linearity is achieved by producing output currents I.sub.3 and I.sub.4 as sums of the collector currents with an offset ratio of 1:4 from the transistors of the emitter-coupled pairs 140 and 150, the offset being caused by the fact that these emitter-coupled pairs 140 and 150 comprise transistors with an emitter area ratio of 1:4.
FIG. 3 shows the input-output characteristic of this differential amplifier contrasted with that of the conventional one. In FIG. 3 curve A is the characteristic curve of the differential amplifier of FIG. 2 while curve B is the characteristic curve of the differential amplifier of FIG. 1, and R.sub.L is the resistance of the load. By comparing these two characteristic curves, it can be seen that the range of input levels with the output distortion up to 1% has been increased from .+-.17 mVpp for the differential amplifier of FIG. 1 to .+-.48 mVpp for that of FIG. 2.
By constructing a gyrator or a biquad filter with such a differential amplifier of the improved linearity, an improvement can be made in a frequency characteristic by regarding the differential amplifier as a single stage integrator, but obtaining a high direct current gain becomes difficult. The lowering of direct current gain in the integrator of an electric filter causes lowering of the quality Q of the device that includes the electric filter, as can be seen from a comparison to a passive filter comprised of an LC circuit.
To cope with this difficulty, a differential amplifier with its output terminals connected, not directly to bases of another differential amplifier but through emitter-followers to bases of another differential amplifier so as to prevent the lowering of direct current gain has been proposed by K. W. Moulding et al. in "Gyrator Video Filter IC with Automatic Tuning" IEEE Journal of Solid State Circuits, Vol. SC-15, No. 6, pp. 963-968, Dec. 1980.
But, connecting the differential amplifier of FIG. 2 to an emitter-follower is equivalent to connecting a transistor with an emitter area five times larger than the minimal emitter area available. Since the base-emitter capacitance of a transistor is proportional to the emitter area, when the emitter area is five times larger as in this case, the base-emitter capacitance also becomes five times greater. Here, it is not possible to reduce the base-emitter capacitance by reducing the base-emitter capacitance of the transistor of a connecting differential amplifier because a base-emitter capacitance of a transistor, which typically is 1 pF-5 pF, is determined by the smallest size manufacturable which is dictated by the manufacturing process. Thus, in this case the increase in the base-emitter capacitance is unavoidable.
Also, in general, it is ideal for an integrator to possess a pole at a very low frequency and no other poles or zeros at any other frequencies. But, since an actual integrator possesses a number of poles and zeros due to the limited quality of transistors incorporated, it is necessary in order to produce a good electric filter that these poles and zeros are at frequencies 50 to 100 times that of the cutoff frequency of the filter. This means if an electric filter were to have a cutoff frequency of 10 MHz, a second pole or zero have to be at 500 MHz to 1 GHz. In other words, it is necessary to take into consideration frequencies much higher than those used in order to produce a good electric filter.
Now, the aforementioned differential amplifier with its output terminals connected to emitter-followers can be considered as a low-pass filter shown in FIG. 4(A) or its equivalent circuit shown in FIG. 4(B) formed by a base-emitter capacitance C.sub.be and output resistance r.sub.o and a base resistance r.sub.b of the emitter-follower 157. In FIG. 4, V.sub.cc is the power source voltage, V.sub.in is an input voltage, and V.sub.out is an output voltage.
In this configuration, there is a pole at the frequency ##EQU1## and if the differential amplifier of FIG. 1 was used with a collector current for the emitter-followers 57 of 0.5 mA, a base-emitter capacitance C.sub.be of 2 pF, and a base resistance r.sub.b of 100 .OMEGA.;, then since EQU r.sub.o =1/g.sub.m =52.OMEGA. (2)
the pole frequency is ##EQU2## On the other hand, if a differential amplifier of FIG. 2 was used with a collector current for the emitter-follower 57 of 1 mA and a base resistance r.sub.b of 40 .OMEGA., then since EQU C.sub.be =2 pF.times.5=10 pF EQU r.sub.o =1/g.sub.m =26.OMEGA. (4)
the pole frequency is ##EQU3## which is less than a half of the previous case, and for the reason explained above, this implies a considerably inferior frequency characteristic.
The preceding arguments show that constructing an emitter-coupled pair by transistors with an emitter area ratio of 1:4 necessitates the use of a transistor with an emitter area four times larger than the minimum size available and this causes the increase in the base-emitter capacitance C.sub.be which deteriorates the frequency characteristic at the high-frequency range.
In addition, it is necessary to drive a differential amplifier with a power source with very low impedance in order to operate it at a high-speed. This is quite disadvantageous because this means that if the base-emitter capacitance C.sub.be in the last example was 5 pF and the pole frequency f.sub.p was to be at 500 MHz, then the collector current of the emitter-follower 157 would have to be 4 mA, so that not only the power consumption increases considerably, but also the base current of the emitter-follower 157 becomes prohibitive.
Furthermore, since the increase in an emitter area causes the lowering of a cutoff frequency, such an amplifier is not suitable for any device that requires a high-speed operation.
On the other hand, in a device requiring a high S/N ratio, the size of the transistor is increased in order to reduce base resistance. Now, with a differential amplifier with transistors having an emitter area ratio as much as 1:4, the noise level is determined by the base resistance of the transistor with the smaller emitter area which in this case has the higher base resistance. But considering the required frequency characteristic and the designed device size, the highly restricted limit on the allowable increase in the size of a transistor makes this type of a differential amplifier unfavourable even in this respect regarding the noise unless the increase in the manufacturing cost were to be overlooked.